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NumericalAlgebraicGeometry :: randomSd(List)

randomSd(List) -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials Ti such that deg(Ti) = di. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.

i1 : T = randomSd {2,3}

                              2                                              
o1 = {(.120541 - .331553*ii)x1  + (- .208092 - .45355*ii)x1*x2 + (- .197452 +
     ------------------------------------------------------------------------
                  2                                          
     .193784*ii)x2  + (.3042 - .0671806*ii)x1*x3 + (- .3619 +
     ------------------------------------------------------------------------
                                                   2             
     .0672645*ii)x2*x3 + (.0974499 - .0873369*ii)x3 , (.0223202 -
     ------------------------------------------------------------------------
                  3                              2                  
     .171298*ii)x1  + (- .0628562 + .394051*ii)x1 x2 + (- .0348928 -
     ------------------------------------------------------------------------
                      2                            3              
     .0313318*ii)x1*x2  + (.0787291 + .277846*ii)x2  + (.0275615 -
     ------------------------------------------------------------------------
                 2                                                   
     .22445*ii)x1 x3 + (.730233 - .0951463*ii)x1*x2*x3 + (- .163376 +
     ------------------------------------------------------------------------
                   2                                  2                
     .0696231*ii)x2 x3 + (- .210458 - .434961*ii)x1*x3  + (- .0534728 +
     ------------------------------------------------------------------------
                     2                             3
     .634964*ii)x2*x3  + (- .178409 + .105398*ii)x3 }

o1 : List
i2 : (S,solsS) = goodInitialPair T;
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{-.243624+.28749*ii, -.151299+.0041826*ii, .913831+.00073*ii}}

o3 : List

See also